If done correctly this is a great way to replace damaged item without a cost to the host.

It was explained that they're not running a for-profit since no rent or fees are charged to the patients, the company has a large donation pool that covers operating costs and staff.

I've seen lead remediation costs under $1k and I've also seen them above $40k.

If you had the funds available, with some cushion, is it advisable to skip the HML and $7-12k cost, and purchase in cash?

Real Estate is definitely not just a "numbers analysis" and you are definitely thinking about things the right way - but I think a good next step for you would be to spend some time putting a lot of this stuff into a (very) basic financial model/spreadsheets mapping out all the potential costs and estimates on effect (effect on value, on exit, different scenarios) - I think getting started with that framework should help with these decisions immensely

Be aware, though, that if your main goal with putting properties into an LLC is to silo off assets to protect yourself in case of litigation, then you need to also set up new bank accounts for each LLC and run all rents and costs through those accounts.

While quick closings can be advantageous, they might come with higher costs or less favorable terms, impacting the financial health of the investment over time.

It's pretty hard to invest with $8k since most lenders have a $100k minimum loan amount, meaning you will need about $35k to buy a property after the 20% down and the associated closing costs. 

These are real costs that hit your bottom line whether you like it or not.The biggest mistake I see from new investors is taking the revenue and minusing the mortgage payment and calling that cash flow.

In my opinion, the most effective approach is to close on the property and take title.